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A241132 Number of partitions p of n such that (maximal multiplicity over the parts of p) = (number of numbers in p having multiplicity > 1). 2

%I #4 Apr 29 2014 18:03:51

%S 0,0,0,0,0,0,1,0,1,1,4,2,5,6,10,16,17,23,32,42,53,79,88,117,146,189,

%T 230,298,374,452,562,688,842,1036,1256,1520,1876,2225,2688,3226,3875,

%U 4608,5528,6553,7799,9272,10936,12903,15239,17919,21038,24714,28922

%N Number of partitions p of n such that (maximal multiplicity over the parts of p) = (number of numbers in p having multiplicity > 1).

%e a(10) counts these 4 partitions: 4411, 42211, 3322, 33211.

%t z = 30; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]];

%t m[p_] := Max[Map[Length, Split[p]]]; Table[Count[IntegerPartitions[n], p_ /; m[p] == e[p]], {n, 0, z}]

%Y Cf. A241090, A241131.

%K nonn,easy

%O 0,11

%A _Clark Kimberling_, Apr 24 2014

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Last modified February 24 11:15 EST 2024. Contains 370303 sequences. (Running on oeis4.)